A barrel has 100 litres of pure alcohol. 20 litres of alcohol is removed and replaced with the same amount of water. This process is repeated two more times. What is the amount of alcohol in the resultant solution?
• a)
40 litres
• b)
36 litres
• c)
51.2 litres
• d)
54.6 litres

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 Ayashkant Dwibedy Mar 29, 2020
Hey aarushi, there's a simple formula to this. Let a be the quantity of alcohol, b be the quantity removed and n be the no. of times operation is performed. Then,
fraction of original liquid(alcohol) left=(a-b/a) raised to the power n times.

Here, fraction of alcohol left= (100-20/100) to the power 3= 0.512
0.512 of 1= 51.2% of original amount.

 Wizius Careers Feb 18, 2022
The above solution of alcohol has been successively diluted three times. Hence we use the formula for successive dilution.

Where v is the initial volume of pure alcohol, c is the concentration of the alcohol after replacements and x is the volume of alcohol replaced.

51.2 litres
Hence, option 3.

 Chint Kumar Jan 21, 2022

 Spiritual Rasoi Jan 15, 2022
We can use the formula
Quantity left = Quantity present initially * ( 1 - quantity removed/ original quantity) raise to power n.

where n = number of iterations.

Quantity left = 100 * ( 1 - 20/100) ^ 3 = 51.2litres

Hey aarushi, there's a simple formula to this. Let a be the quantity of alcohol, b be the quantity removed and n be the no. of times operation is performed. Then,fraction of original liquid(alcohol) left=(a-b/a) raised to the power n times. Here, fraction of alcohol left= (100-20/100) to the power 3= 0.5120.512 of 1= 51.2% of original amount.Hence answer is c)

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